tocsectionReference

Key terms
To provide common ground for discussion with readers of various backgrounds, we list the specification of key terms related to the methods in Supplemental materials. The following list provides explanations at an intuition level without the attempt to establish formal definitions. Readers could refer to referenced materials for more formal definitions.
Deep learning specific

model architecture: the design of a model as a set of trainable parameters without specification on the exact weight of the parameters [1]}.

loss landscape: the geometry of the global loss associated with a model architecture[2]}.

model instance: given a model architecture with certain amount of trainable parameters, a set of weights associated to the trainable parameters defines an instance of model; during the training process, each optimization step leads to a model instance.

optimization[1]}: neural network is trained by optimizing a object function, usually in the form of minimizing a loss function.

global/local optimum: under the optimization formalization, the optimum point is at the end of the optimization process. As explained in [4]}, in an ideal world where the complete distribution of data is available to train a model, the optimum is global; while any stop point for any certain subdistribution is a local optimum.

model initialization: optimization always starts with an initialization of an model instance.

pretraining[5]}: train a model on a pretext task before training on the target task; the trained model instances will become the initialization of the target task.

finetuning[5]}: train a model on a target task with initialization pretrained task.

Independent and Identifically distributed (IID)[7]}: if given a set of data \({x_i}\) , each of these \(x_i\)  observations is an independent draw from a fixed (“stationary”) probability distribution.

Out-of-distribution (OOD) generalization[8]}: Generalization consists in reducing the gap in performance between training data and testing data. When the data generating process from the training data is indistinguishable from that of the test data, it's “in-distribution”, if not, it's called out-of-distribution generalization problem [8]}. As in [10]}, considering datasets \(Data_{e}:=\lbrace (x_{i}^{e},y_{i}^{e} )\rbrace _{i=1}^{n_{e}}\)  collected under multiple domains \(e\) , each containing samples IID with a probability distribution \(D(X^{e},Y^{e})\) . The goal of OOD generalization is to use these datasets to learn a predictior \(Y\approx f(X)\) , which performs well across a large set of unseen but related domains \(e\in \mathcal {E}_{all}\) . Namely, the goal is to minimize
\(R^{OOD}(f) = \max _{e\in \mathcal {E}_{all}} R^{e}(f)\) 
, where
\(R^{e}(f) := E_{X^{e}, Y^{e}}[l(f(X^{e}),Y^{e})]\) 
is the risk under domain \(e\) . Here the set \(\mathcal {E}_{all}\)  contains all possible domains.

generalization[1]}: the most general goal of generalization is to enable the model make reliable prediction on unseen data; out-of-distribution prediction (OOD) is a more challenging type of generalization problem which requires the model to be generalizable to unseen data distribution.

mini-batch[1]}: as a common practice for robustness and computation memory concerns, no matter how large a data set is available, only a sub set of data is sampled to train a model at each optimization step.

representation[1]}: as coined by the line of work named “representation learning”, the word representation is interachangable with “embedding”, referring to a vector/matrix of learned features.

transfer model parameter: a technique that is related to pretraining-finuetuning; for the implementation, a simple initialization of part of the target model using the pretrained model could serve the purpose.

Chemical-protein interaction (CPI) specific

CPI prediction: formulated as a binary classification task, to predict whether or not a pair of protein and chemical will bind given only protein sequence and chemical SMILES string.

protein descriptor, chemical descriptor: the modules of a whole CPI prediction model to extract protein/chemical embedding in a euclidean space.

Portal learning specific

universe: a model architecture that defines a data transformation space, together with a data set.

portal: a model instance in a universe—which could be a local optimum in the current universe, but which facilitates moving the model to the global optimum in the ultimately targeted universe.

local loss landscape: optimize a model on a sub-distribution of the complete underlying distribution of the whole data set.

global loss landscape: the direction of gradient search towards global optimum for all sub-distributions.

stress test: a technique[14]} to evaluate a predictor by observing its outputs on specifically designed inputs; three common types are stratified performance evaluation, shifted evaluation and contrastive evaluation.

shifted evaluation[14]}: the stress test employed in this paper, which splits train/test data set by Pfam families, i.e. proteins in the testing and training sets come from different Pfam families. This is a simple simulation off dark space model deployment.

deployment gap: the difference between the performance evaluated by the test set and that evaluated by the development set.

classic deep learning training scheme: randomly split a whole data set into train/dev/test set; optimize model on a randomly sampled mini-batch data; choose a final trained model instance based on the best test evaluation metrics; usually adopts empirical risk minimization [16]} formulation.


Methods: PortalCG in four-universe configuration for dark chemical genomics space
In this section, we present the detailed methodology used in portal learning in the context of a four-universe configuration.
Data preprocessing 
The four-universe configuration is built on three major databases, Pfam[17]}, Protein Data Bank (PDB)[18]}, BioLp[19]} and ChEMBL[20]}. The data were preprocessed as follows.

Protein sequence universe. All sequences from Pfam-A families are used to pretrain the protein descriptor following the same setting in DISAE [21]} that highlights a MSA-based distillation process.

Protein structure universe. In our protein structure data set, there are 30,593 protein structures, 13,104 ligands, and 91,780 ligand binding sites. Binding sites were selected according to the annotation from BioLip (updated to the end of 2020). Binding sites which contact with DNA/RNA and metal ions were not included. If a protein has more than one ligand, multiple binding pockets were defined for this protein. For each binding pocket, the distances between \(C\alpha \)  atoms of amino acid residues of the binding pocket were calculated. In order to obtain the distances between the ligand and its surrounding binding site residues, the distances between atom i in the ligand and each atom in the residue j of the binding pocket were calculated and the smallest distance wa selected as the distance between atom i and residue j. In order to get the sequence feature of the binding site residues in the DISAE protein sequence representation[21]}, binding site residues obtained from PDB structures (queries) were mapped onto the multiple sequence alignments of its corresponding Pfam family. First, a profile HMM database was built for the whole Pfam families. hmmscan [23]} was applied to search the query sequence against this profile database to decide which Pfam family it belongs to. For those proteins with multiple domains, more than one Pfam families were identified. Then the query sequence was aligned to the most similar sequence in the corresponding Pfam family by using phmmer. Aligned residues on the query sequence were mapped to the multiple sequence alignments of this family according to the alignment between the query sequence and the most similar sequence.

Chemical universe. All chemicals in the ChEMBL26 database consists of the chemical universe.

Protein function universe. CPI classification prediction data is the whole ChEMBL26[20]} database where the same threshold for defining positive and negative labels creating as that in DISAE [21]} was used.


Algorithm 
In the four-universe configuration, portal learning starts with portal identification in the protein sequence universe, then travels into protein structure universe for portal calibration before finally comes into the target protein function universe, where OOC-ML will be invoked for model optimization. Along the way, shifted evaluation, one type of stress model selection, is used to select the “best” model instance, which splits train/test based on Pfam families, i.e. training set and testing set have proteins come from different Pfam families. Each phase will be specified in the following sections.
Chemical representation
A chemical was represented as a graph and its embedding was learned using GIN[26]}.

Protein sequence pre-training
Protein descriptor is pretrained from scratch following exactly DISAE [21]} on whole Pfam families, making it a universal protein language model. With standard Adam optimization, shifted evaluation is used to select the “best” instance.

Protein structure regularization
With the protein descriptor pretrained using the sequences from the whole Pfam, chemical descriptors and a distance learner were plugged in to fine-tune the protein representation. The distance learner follows Alphafold[28]} which formulates a multi-way classification on a distrogram. Based on the histogram of binding site distances, a histogram equalizationHistogram equalization: https://en.wikipedia.org/wiki/Histogram_equalization was applied to formulate a 10-way classification on our binding site structure data as in Supplemental material Figure S REF . Since protein and chemical descriptors output position-specific embeddings of a distilled protein sequence and all atoms of a chemical, pair-wise interaction features on the binding sites were created with a simple vector operation: a matrix multiplication was used to select embedding vectors of each binding residue and atom; multiply and broadcast the selected embedding vectors into a symmetric tensor as shown in the following, where \(H\)  is embedding matrix of size \((number\_of\_residues, embedding_dimension)\)  or \((number\_of\_atoms, embedding_dimension)\)  and \(A\)  is selector matrix[29]},
\(H_{binding\_site}^{protein} = A^{protein}*H_{full\_distilled}^{protein}\) 
\(H_{binding\_site}^{chemical} = A^{chemical}*H_{full\_chemical\_graph}^{chemical}\) 
\(H_{binding\_site}^{interaction} = (H_{binding\_site}^{protein})^{T} *H_{binding\_site}^{chemical}\) 
This pair-wise interaction feature tensor \(H_{binding\_site}^{interaction}\)  was fed into a Attentive Pooling[30]} layer followed by feed-forward layer for final 10-way classification. Detailed model architecture configuration could be found in Table S REF  and Figure SREF  .The intuition for the simplest form of distance learner is to put all stress of learning on the shared protein and chemical descriptors which will carry information across universes. Again, with standard Adam optimization, shifted evaluation was used to select the “best” instance. Two versions of distance structure prediction were implemented, one formulated as a binary classification, i.e. contact prediction, one formulated as a multi-way classification, i.e. distogram prediction. The performance of the two version are similar, as shown in Figure S REF .

Out-of-cluster Meta Learning (OOC-ML) in protein function universe
With fine-tuned protein descriptor in the protein function universe, a binary classifier is plugged on, which is a ResNet[31]} layered with two linear layers as shown in Table S REF  and Figure SREF . What plays the major role in this phase is the optimization algorithm OOC-ML as shown in pseudocode Algorithm1 and main content Figure 1(B),(C.1). The local loss landscape exploration is reflected in line 4-9, and line 10 shows ensemble of global loss landscape. Note that more variants could be derived from changing sampling rule (line 3 and 5) and global loss ensemble rule.
OOC-ML is built on MAML[32]} but has significant differences. Echoing to steps illustrated in the Figure 1 of the main text:

As shown in main content Figure1 (B), OOC-ML has a sub-distribution data split into support set and query set, or as MAML named it, meta-train and meta-test within training set and test set. However, MAML sub-distributions are identified from the label space \(\lbrace Y\rbrace \)  while OOC-ML identifies sub-distributions, i.e. clusters, from input feature space \(\lbrace X\rbrace \) . In PortalCG, the clusters are identified by Pfam. Further, OOC-ML allows the utilization of very small clusters where very limited known data points are available for training. For example, in PortalCG, some Pfam families with too few samples to be split into support and query set are organized as query-set-alone, which participate only in the global loss optimization, as detailed below.

In each mini-batch, a few sub-distributions are sampled. The whole optimization has two layers, inner loop and outer loop. At the inner loop, each sub-distribution data has its own local loss landscape. The support set is used for in-distribution optimization on the local loss landscape.

The locally optimized model is then used on query set to get a query set loss, which will be fed to the global loss landscape. Each sub-distribution is independently optimized. This step is the same as MAML. What is different is that OOC-ML also calculates query-set without local in-distribution optimization for the small clusters.

Local query set losses are pooled together and the model will be optimized on the global loss landscape as meta-optimization defined in MAML.

After finishing train, the model will be deployed.

MAML is designed for multi-class classification in few-shot learning, at deployment stage, it's expected to meet new unseen class. And it's assumed that there are a few labelled sample available as support set, hence named as few-shot learning. For each unseen class, the trained model will carry out a fast in-distribution adaptation using support set before final prediction on the query set. However, this is impossible in the context of dark space illumination. Portal learning trained model has to make robust predictions without any chance of in-distribution adaptation.

1em
[ht]
LeftleftThisthisUpup
UnionUnionFindCompressFindCompress
InputinputOutputoutput
\(\alpha ,\beta \) , learning step size hyperparameters;
\(L\) , number of optimization steps in each round of local exploration;
\(T\) , number of global training steps;
\(K\) , number of points sampled from a local neighborhood

\(\theta \)  the whole model weights
initialization whole model weights \(\theta \)  (with weight transfered from portal for protein and chemical descriptors and random initiliazed weights for binary classifier)
\(t\)  in \(T\) 
Sample a \(D_i \sim p(D)\) ;
\(l\)  in \(L\) 
Sample a positive-negative balanced mini-batch of \(K\)  pairs \(neighborhood_m \sim D_i\) ;
\(point_j\)  in \(neighborhood_m\)  
Evaluate \(\nabla _{\theta } L_{point_j}(f_\theta )\)  with respect to \(K\)  examples
Compute adapted parameters with gradient decent:\(\theta _{i}^{^{\prime }}= \theta - \alpha \nabla _{\theta }L_{point_j}(f_\theta )\) 

Update \(\theta \leftarrow \theta - \beta \nabla _{\theta }\sum _{D_{i}\sim p(D)}L_{point_j}(f_{\theta }^{^{\prime }})\)
Portal Learning Optimization Algorithm: Out-of-cluster Meta-learning

Stress model instance selection
In classic training scheme common practice, there are 3-split data sets, “train set”, “dev set” and “test set”. Train set as the name suggested is used to train model. Test set as commonly expected is used to set an expectation of performance when applying the trained model to unseen data. Dev set is to select the preferred model instance. In OOD setting, data is split (main content Table 1) such that dev set is a OOD from train set and test set is a OOD from both train and dev set. Deployment gap is calculated by deducting ODD-dev performance with OOD-test performance.

Implementation details
With portal learning being a framework, all experiments are based on the configuration of a four-universe design. Four major variants of models are trained as shown in main content Table 2 for controlled factor experiments to verify the contribution of key components of Portal Learning. In this section we present implementation details.
Due to the large number of total samples, all training are carried out under global step-based formalization instead of epoch-based. Typically, a deep learning model is trained for numerous epochs, in each epoch the model will loop over all training data. Evaluation will be carried out once on the whole test data set at the end of each epoch. In the global step formalization, a mini-batch is sampled at uniform random from pre-split training data set. For a pre-defined total number of global steps, this mini-batch sampling will be repeated. Training is stopped when loss decreases are within a pre-defined error margin. To evaluate along the way of training, for every \(m\)  global steps of training, a subset of test data is sampled uniformly randomly from a pre-split test set. To compute generalization gaps, in addition to evaluate on test set split according to the shifted evaluation, a dev set is held out from the train set for the evaluation as well. In this way, dev set and train set are iid. The performance difference between dev and train is the observed space generalization gap while the performance difference between dev and test is the dark space generalization gap.

Evaluation metrics
Distogram prediction uses an average accuracy on the distogram. CPI binary classification uses F1, ROC-AUC and PR-AUC for overall evaluation with breakdown by class F1, recall and precision scores.

Docking as baseline
Protein-ligand docking was performed using Autodock Vina[33]}. The whole protein surface search implemented in the Autodock Vina was applied to identify the ligand binding pocket. The center of each protein was set as the center of the binding pocket. The largest distance of the protein atoms to the center of the protein is calculated for each x, y, and z direction to define the edge of each protein. 10 Angstrom of extra space was added to the protein edge to set up the search space for the docking.

Production level for deployment
To create a production level model, three models were trained in PortalCG with only difference in data split. Dev set was OOD in respect of training set to make sure there was no overlapped Pfam families between them. By rotating Pfam families between training set and OOD-dev set in the fashion of a cross-validation, each of the three models was trained on different train set in light of Pfam families involved. Then a voting mechanism was used to make the final prediction.

Dark space exploration from a theoretical lens
A neural network classifier is trained by minimizing a loss function with a standard form as the following:
\(L(\theta ) = \frac{1}{|D_t|} \sum _{(x,y)\in D_t} -\log p_{\theta }(x,y)\) 
where \(p_{\theta }(x,y)\)  is the probability that a sample \(x\)  belongs to the class \(y\)  according to the trained neural network with parameters \(\theta \) , and \(D_t\)  is the training data set with the number of samples \(|D_t|\) . As laid out in the recent framework in [4]} that reasons about generalization in deep learning, the test error of a model \(f_{t}\)  could be decomposed as follows,
\(TestError(f_{t}) = \underbrace{TestError(f_{t}^{iid})}_\text{ideal world} +\underbrace{[TestError(f_{t}) - TestError(f_{t}^{iid})]}_\text{real world generalization gap}\) 
When data are sampled as independent and identically distributed (iid) random variables, “ideal world” is a scenario where the complete data distribution is available with infinite data and optimization is on a population loss landscape. By contrast, “real world” has only finite data, where optimization is on an empirical loss landscape.
In the dark space context of the OOD setting, this decomposition needs to be changed to
\(TestError(f_{t}^{OOD}) = \underbrace{TestError(f_{t}^{iid})}_\text{observed space} +\underbrace{[TestError(f_{t}^{OOD}) - TestError(f_{t}^{iid})]}_\text{dark space generalization gap}\) 
and
\(TestError(f_{t}^{iid}) = TrainError(f_{t}^{iid}) +\underbrace{[TestError(f_{t})^{iid} - TrainError(f_{t}^{iid})]}_\text{observed space generalization gap}\) 
This explains that the effort could be devoted to decrease the observed space error and/or the dark space generalization gap to reduce \(TestError(f_{t}^{OOD})\) .
\(\nabla _{\theta }J(\theta ) \approx g= \frac{1}{m}\sum _{i=1}^{m}\nabla _{\theta }L(x^{(i)} , y^{(i)},\theta )\) 
\(\theta \leftarrow \theta - \epsilon g\) 
When stochastic gradient descent (SDG) is applied to the optimization, it approximately estimates \(\nabla _{\theta }J(\theta )\) , the expectation of gradient, using a small set of sample of size \(m\) , i.e., the mini-batch drawn uniformly from the training set. When all data are IID, this approximation works fine to update \(\theta \)  with \(g\) . However, for the ODD with unknown distribution, this \(\theta \)  updating function could easily fall into a local minimum based on the \(m\)  mini-batch samples.
The test error for a trained model in the OOD setting includes two parts: test errors in the observed IID space and a generalized gap when stepping into the OOD space. Furthermore, as discussed and proved in [8]}, [10]}, not all OOD tasks are equal. Depending on how different the OOD data set is from the train set, some OOD task could be more challenge. It is true for predicting ligand binding to dark proteins. It is impossible for training data to provide sufficient coverage of the whole distribution in the dark chemical genomics space. The motivation of Portal Learning for exploring the dark space follows: one model architecture defines a functional mapping space, together with a data set defines a universe. The model initialized instance in a universe closer to the global optimum universe is a portal that is transferred from an associated universe. CPI dark space is impossible to be explored if the learning is confined only in the observed protein function, i.e. CPI universe since the known data are far sparse as shown in main content Figure 3. Hence STL is important to identify portals. The model optimization on a loss function can decrease IID training errors but will not help with the observed IID space generalization gap \(TestError(f_{t})^{iid} - TrainError(f_{t}^{iid})\)  or the dark space generalization gap \(TestError(f_{t}^{OOD}) - TestError(f_{t}^{iid})\) . With Portal Learning, stress model instance selection can narrow the first gap and OOC-ML can narrow the second gap.

Additional tables
tocsubsectionTable REF : Drugs predicted to interact with SARS-COVID-2 interactors
<TABLE>tocsubsectionTable : Undruggable human disease-associated proteins selected by ProtalCG
@|l|C6.5cm|l|l|@
Uniprot  Protein name  Drug name  Probscore
4cTable S1 continued from previous page
Uniprot  Protein name  Drug name  Probscore
Q8TEX9  Importin-4  fenebrutinib  0.68089414
Q8NB66  Protein unc-13 homolog C  AI-10-49  0.67951804
Q9NZF1  Placenta-specific gene 8 protein  AI-10-49  0.6778485
Q96G03  Phosphoglucomutase-2  fenebrutinib  0.677423
Q8IWU4  Zinc transporter 8  fenebrutinib  0.677423
P53004  Biliverdin reductase A  AI-10-49  0.6769635
P40879  Chloride anion exchanger  fenebrutinib  0.67688245
Q8IYL2  Probable tRNA  fenebrutinib  0.6768823
Q9ULL4  Plexin-B3  AI-10-49  0.67652583
Q96SZ6  Mitochondrial tRNA methylthiotransferase CDK5RAP1  fenebrutinib  0.6763639
Q9BRT9  DNA replication complex GINS protein SLD5  fenebrutinib  0.6763639
Q8N2U0  Transmembrane protein 256  CCT137690  0.67634773
Q9UC06  Zinc finger protein 70  fenebrutinib  0.6761195
Q9BPX5  Actin-related protein 2/3 complex subunit 5-like protein  Q-203  0.67571765
Q8TDF6  RAS guanyl-releasing protein 4  NMS-1286937  0.6756182
Q9P2G3  Kelch-like protein 14  NMS-1286937  0.6756182
Q9HBT7  Zinc finger protein 287  CCT137690  0.6752016
Q9UKR8  Tetraspanin-16  PF-05190457  0.6751168
P59044  NACHT, LRR and PYD domains-containing protein 6  MK-5046  0.67498016
Q16774  Guanylate kinase  MK-5046  0.6749801
Q9HCE5  N6-adenosine-methyltransferase non-catalytic subunit  PF-05190457  0.67497396
Q15185  Prostaglandin E synthase 3  cilofexor  0.6745854
Q8WUA7  TBC1 domain family member 22A  fenebrutinib  0.67439413
Q17RS7  Flap endonuclease GEN homolog 1  CGM097  0.67434615
Q14244  Ensconsin  PF-05190457  0.67431164
Q9BRK5  45 kDa calcium-binding protein  PF-05190457  0.67431164
Q9UKJ5  Cysteine-rich hydrophobic domain-containing protein 2  CCT137690  0.67429835
Q6ZWJ1  Syntaxin-binding protein 4  AI-10-49  0.6742442
Q9HAR2  Adhesion G protein-coupled receptor L3  AI-10-49  0.67414063
P98161  Polycystin-1  AI-10-49  0.67414063
Q92673  Sortilin-related receptor  AI-10-49  0.6740716
D6RGH6  Multicilin  fenebrutinib  0.67397785
Q8NHH9  Atlastin-2  fenebrutinib  0.67395777
Q9H0E2  Toll-interacting protein  PF-05190457  0.6739072
O15145  Actin-related protein 2/3 complex subunit 3  PF-05190457  0.6739072
P51116  Fragile X mental retardation syndrome-related protein 2  abemaciclib  0.6738332
Q9BR09  Neuralized-like protein 2  elbasvir  0.67369795
P42568  Protein AF-9  AI-10-49  0.67364717
P17600  Synapsin-1  AI-10-49  0.67364717
P48553  Trafficking protein particle complex subunit 10  AI-10-49  0.6736086
Q12955  Ankyrin-3  abemaciclib  0.6735056
O60936  Nucleolar protein 3  abemaciclib  0.6735056
Q02575  Helix-loop-helix protein 1  AI-10-49  0.6734969
P49640  Homeobox even-skipped homolog protein 1  CFI-402257  0.67348343
P22670  MHC class II regulatory factor RFX1  PF-05190457  0.67346805
Q8IUF8  Ribosomal oxygenase 2  NMS-1286937  0.67343307
P22681  E3 ubiquitin-protein ligase CBL  NMS-1286937  0.67343307
Q7RTS3  Pancreas transcription factor 1 subunit alpha  MK-5046  0.67334837
Q9Y5L4  Mitochondrial import inner membrane translocase subunit Tim13  NMS-P715  0.6733338
P17735  Tyrosine aminotransferase  PF-05190457  0.673238
O95294  RasGAP-activating-like protein 1  PF-05190457  0.673224
Q8NCD3  Holliday junction recognition protein  PF-05190457  0.673224
Q86W28  NACHT, LRR and PYD domains-containing protein 8  MK-5046  0.6731598
Q04671  P protein  AI-10-49  0.67310166
Q9C035  Tripartite motif-containing protein 5  AI-10-49  0.6731016
Q66K64  DDB1- and CUL4-associated factor 15  AI-10-49  0.672944
Q5T9A4  ATPase family AAA domain-containing protein 3B  CFI-402257  0.67286545
Q96MP8  BTB/POZ domain-containing protein KCTD7  CFI-402257  0.6728654
Q9UIE0  Zinc finger protein 230  CFI-402257  0.672853
Q3SYG4  Protein PTHB1  abemaciclib  0.67280704
Q8IUY3  GRAM domain-containing protein 2A  AI-10-49  0.67273754
O75689  Arf-GAP with dual PH domain-containing protein 1  AI-10-49  0.67273754
Q9NZP8  Complement C1r subcomponent-like protein  fenebrutinib  0.6727066
Q9NQX4  Unconventional myosin-Vc  fenebrutinib  0.6727064
Q15388  Mitochondrial import receptor subunit TOM20 homolog  CFI-402257  0.6726911
Q9NXL9  DNA helicase MCM9  piperaquine-phosphate  0.6726752
P53370  Nucleoside diphosphate-linked moiety X motif 6  piperaquine-phosphate  0.6726752
Q8N7C0  Leucine-rich repeat-containing protein 52  PF-05190457  0.67262363
O95231  Homeobox protein VENTX  NMS-P715  0.67261267
Q9HC56  Protocadherin-9  AI-10-49  0.6725752
A6NNW6  Enolase 4  AI-10-49  0.6725752
P35612  Beta-adducin  CFI-402257  0.67255336
Q9Y6M5  Zinc transporter 1  AI-10-49  0.67255074
Q01804  OTU domain-containing protein 4  AI-10-49  0.6725507
Q9Y678  Coatomer subunit gamma-1  MK-5046  0.67254347
Q9BTY7  Protein HGH1 homolog  AI-10-49  0.67243195
Q8NEM0  Microcephalin  CFI-402257  0.6724283
Q7LGA3  Heparan sulfate 2-O-sulfotransferase 1  AI-10-49  0.67242616
O75956  Cyclin-dependent kinase 2-associated protein 2  ziritaxestat  0.6723895
P62987  Ubiquitin-60S ribosomal protein L40  ziritaxestat  0.6723893
Q14257  Reticulocalbin-2  CDK9-IN-6  0.6723883
Q9H0I3  Coiled-coil domain-containing protein 113  tropifexor  0.6723477
P32019  Type II inositol 1,4,5-trisphosphate 5-phosphatase  fenebrutinib  0.6723469
O95409  Zinc finger protein ZIC 2  fenebrutinib  0.6723469
P56179  Homeobox protein DLX-6  fenebrutinib  0.67233485
Q12798  Centrin-1  AI-10-49  0.6722851
Q14714  Sarcospan  AI-10-49  0.6722851
Q96LI5  CCR4-NOT transcription complex subunit 6-like  abemaciclib  0.6722749
Q86XR7  TIR domain-containing adapter molecule 2  AI-10-49  0.6722719
P53672  Beta-crystallin A2  CCT137690  0.6722543
O43439  Protein CBFA2T2  CCT137690  0.6722543
Q9H0E3  Histone deacetylase complex subunit SAP130  fenebrutinib  0.6722474
Q8NFZ0  F-box DNA helicase 1  fenebrutinib  0.6722474
Q8N0S2  Synaptonemal complex central element protein 1  CFI-402257  0.67223567
Q92667  A-kinase anchor protein 1, mitochondrial  fenebrutinib  0.67222863
O60884  DnaJ homolog subfamily A member 2  PF-05190457  0.6721347
P41214  Eukaryotic translation initiation factor 2D  AI-10-49  0.6721203
Q6R327  Rapamycin-insensitive companion of mTOR  AI-10-49  0.67211396
O75886  Signal transducing adapter molecule 2  PF-05190457  0.67206836
Q9UMX6  Guanylyl cyclase-activating protein 2  PF-05190457  0.6720683
Q99447  Ethanolamine-phosphate cytidylyltransferase  CCT137690  0.67205685
Q6FI13  Histone H2A type 2-A  PF-05190457  0.6720233
Q969S2  Endonuclease 8-like 2  fenebrutinib  0.67200994
Q6XZF7  Dynamin-binding protein  AI-10-49  0.67196065
Q96EX1  Small integral membrane protein 12  fenebrutinib  0.6719141
Q8TD57  Dynein axonemal heavy chain 3  fenebrutinib  0.6719141
O15375  Monocarboxylate transporter 6  PF-05190457  0.6719058
Q9H7E2  Tudor domain-containing protein 3  NMS-1286937  0.6718896
A6NI73  Leukocyte immunoglobulin-like receptor subfamily A member 5  AI-10-49  0.671879
Q9NZM3  Intersectin-2  CDK9-IN-6  0.6718554
O75145  Liprin-alpha-3  CDK9-IN-6  0.6718554
Q9NSD9  Phenylalanine–tRNA ligase beta subunit  abemaciclib  0.6718319
O15195  Villin-like protein  abemaciclib  0.6718319
P05538  HLA class II histocompatibility antigen, DQ beta 2 chain  cilofexor  0.671822
Q8TD57  Dynein axonemal heavy chain 3  cilofexor  0.671822
Q9NRD9  Dual oxidase 1  abemaciclib  0.6718094
Q8WUQ7  Cactin  AI-10-49  0.67178315
Q9H7C4  Syncoilin  AI-10-49  0.67178315
Q70EK9  Ubiquitin carboxyl-terminal hydrolase 51  PF-05190457  0.671742
O43837  Isocitrate dehydrogenase [NAD] subunit beta, mitochondrial  PF-05190457  0.67174196
Q9UKY1  Zinc fingers and homeoboxes protein 1  CFI-402257  0.6717407
Q6ZMJ2  Scavenger receptor class A member 5  CFI-402257  0.6717407
P61371  Insulin gene enhancer protein ISL-1  fenebrutinib  0.6717256
Q6NSZ9  Zinc finger and SCAN domain-containing protein 25  fenebrutinib  0.6717256
Q92754  Transcription factor AP-2 gamma  IACS-10759  0.67171496
Q5RKV6  Exosome complex component MTR3  AI-10-49  0.6716919
Q9BRA0  N-alpha-acetyltransferase 38, NatC auxiliary subunit  MK-5046  0.6716785
Q9BSF8  BTB/POZ domain-containing protein 10  CCT137690  0.67165
Q6PJ69  Tripartite motif-containing protein 65  AI-10-49  0.6716369
Q9NRP0  Oligosaccharyltransferase complex subunit OSTC  AI-10-49  0.6716369
Q8TBM7  Transmembrane protein 254  PF-05190457  0.6716311
Q674X7  Kazrin  elbasvir  0.6716015
Q9Y3C4  EKC/KEOPS complex subunit TPRKB  abemaciclib  0.6715913
P59190  Ras-related protein Rab-15  abemaciclib  0.6715913
Q9NZM3  Intersectin-2  PF-05190457  0.6715465
P05455  Lupus La protein  AI-10-49  0.6715072
Q96KN3  Homeobox protein PKNOX2  abemaciclib  0.67148525
P54278  Mismatch repair endonuclease PMS2  abemaciclib  0.6714852
P49069  Guided entry of tail-anchored proteins factor CAMLG  fenebrutinib  0.6714454
Q8IYT4  Katanin p60 ATPase-containing subunit A-like 2  AI-10-49  0.6714413
Q8WVI0  Small integral membrane protein 4  AI-10-49  0.67144126
Q9Y6X6  Unconventional myosin-XVI  MK-5046  0.6713607
Q8N357  Solute carrier family 35 member F6  MK-5046  0.6713607
Q96BP2  Coiled-coil-helix-coiled-coil-helix domain-containing protein 1  abemaciclib  0.671357
Q9UJQ4  Sal-like protein 4  MK-5046  0.67135173
Q9HCQ5  Polypeptide N-acetylgalactosaminyltransferase 9  fenebrutinib  0.67132807
Q9P2Q2  FERM domain-containing protein 4A  fenebrutinib  0.67132807
Q7Z7M8  UDP-GlcNAc:betaGal beta-1,3-N-acetylglucosaminyltransferase 8  NMS-P715  0.6713157
Q9HCK5  Protein argonaute-4  PF-05190457  0.6713007
O95405  Zinc finger FYVE domain-containing protein 9  AI-10-49  0.67127687
Q92911  Sodium/iodide cotransporter  PF-05190457  0.67127484
Q8WWI1  LIM domain only protein 7  fenebrutinib  0.6712641
Q8N3C7  CAP-Gly domain-containing linker protein 4  fenebrutinib  0.671264
Q9UBS8  E3 ubiquitin-protein ligase RNF14  PF-05190457  0.671259
Q9BY66  Lysine-specific demethylase 5D  PF-05190457  0.671259
Q9UPM8  AP-4 complex subunit epsilon-1  abemaciclib  0.6712124
Q9BYE0  Transcription factor HES-7  MK-5046  0.6711568
Q9BSD7  Cancer-related nucleoside-triphosphatase  AI-10-49  0.67114973
Q9NXH9  tRNA  tropifexor  0.6711371
Q13948  Protein CASP  tropifexor  0.6711371
Q9C019  Tripartite motif-containing protein 15  abemaciclib  0.67111254
Q5TA50  Ceramide-1-phosphate transfer protein  ABT-702  0.6711099
Q7KZF4  Staphylococcal nuclease domain-containing protein 1  ABT-702  0.6711099
P08247  Synaptophysin  fenebrutinib  0.6711092
A4IF30  Solute carrier family 35 member F4  AI-10-49  0.67109805
Q9NRA8  Eukaryotic translation initiation factor 4E transporter  AI-10-49  0.67109805
Q96FF9  Sororin  acalabrutinib  0.6710895
P10073  Zinc finger and SCAN domain-containing protein 22  PF-05190457  0.67107534
P0CW19  LIM and senescent cell antigen-like-containing domain protein 3  PF-05190457  0.67107534
Q9UPM8  AP-4 complex subunit epsilon-1  fenebrutinib  0.6710706
P08118  Beta-microseminoprotein  PF-05190457  0.6710468
Q96P16  Regulation of nuclear pre-mRNA domain-containing protein 1A  fenebrutinib  0.6710315
P62280  40S ribosomal protein S11  piperaquine-phosphate  0.6710226
Q8TE49  OTU domain-containing protein 7A  AI-10-49  0.6710194
Q53HI1  Protein unc-50 homolog  AI-10-49  0.6710194
Q8WW32  High mobility group protein B4  PF-05190457  0.6709929
P57729  Ras-related protein Rab-38  PF-05190457  0.67099285
Q8N2M8  CLK4-associating serine/arginine rich protein  fenebrutinib  0.6709883
P25705  ATP synthase subunit alpha, mitochondrial  fenebrutinib  0.6709781
Q9Y5H3  Protocadherin gamma-A10  PF-05190457  0.6709645
Q9NU63  Zinc finger protein 57 homolog  fenebrutinib  0.67096215
P43363  Melanoma-associated antigen 10  AI-10-49  0.6709133
Q13469  Nuclear factor of activated T-cells, cytoplasmic 2  AI-10-49  0.670904
Q8NG77  Olfactory receptor 2T12  AI-10-49  0.670904
Q9Y2G8  DnaJ homolog subfamily C member 16  PF-05190457  0.67090386
Q9ULV8  E3 ubiquitin-protein ligase CBL-C  fenebrutinib  0.67089945
Q96EF0  Myotubularin-related protein 8  elbasvir  0.67085487
Q8TD16  Protein bicaudal D homolog 2  abemaciclib  0.6708334
P49459  Ubiquitin-conjugating enzyme E2 A  abemaciclib  0.6708334
Q6XZF7  Dynamin-binding protein  AI-10-49  0.6708271
Q9Y4I1  Unconventional myosin-Va  AI-10-49  0.6708271
Q96FL9  Polypeptide N-acetylgalactosaminyltransferase 14  MK-5046  0.67080116
Q9HD67  Unconventional myosin-X  MK-5046  0.6708011
Q13214  Semaphorin-3B  MK-5046  0.6707926
Q53H47  Histone-lysine N-methyltransferase SETMAR  MK-5046  0.6707926
P46776  60S ribosomal protein L27a  AI-10-49  0.67078424
Q15306  Interferon regulatory factor 4  AI-10-49  0.6707842
Q2TAA2  Isoamyl acetate-hydrolyzing esterase 1 homolog  abemaciclib  0.67076474
O43324  Eukaryotic translation elongation factor 1 epsilon-1  PF-05190457  0.67074585
Q96R27  Olfactory receptor 2M4  fenebrutinib  0.6707435
Q5VXU1  Sodium/potassium-transporting ATPase subunit beta-1-interacting protein 2  fenebrutinib  0.6707435
Q5VWQ8  Disabled homolog 2-interacting protein  fenebrutinib  0.67072076
Q9UJF2  Ras GTPase-activating protein nGAP  elbasvir  0.67071134
O75923  Dysferlin  fenebrutinib  0.6707069
O75592  E3 ubiquitin-protein ligase MYCBP2  PF-05190457  0.6706958
Q14714  Sarcospan  CFI-402257  0.67069536
Q12798  Centrin-1  CFI-402257  0.67069536
Q9H9Z2  Protein lin-28 homolog A  fenebrutinib  0.67065567
Q8N2A8  Mitochondrial cardiolipin hydrolase  fenebrutinib  0.67065555
Q5VV41  Rho guanine nucleotide exchange factor 16  abemaciclib  0.6706521
Q96QT6  PHD finger protein 12  fenebrutinib  0.67064524
Q13948  Protein CASP  AI-10-49  0.6706354
Q9NXH9  tRNA  AI-10-49  0.6706354
Q969E2  Secretory carrier-associated membrane protein 4  fenebrutinib  0.67062545
P58107  Epiplakin  fenebrutinib  0.67062545
P55036  26S proteasome non-ATPase regulatory subunit 4  NMS-P715  0.67059726
Q11128  4-galactosyl-N-acetylglucosaminide 3-alpha-L-fucosyltransferase FUT5  AI-10-49  0.6705861
Q86W28  NACHT, LRR and PYD domains-containing protein 8  AI-10-49  0.6705852
O43566  Regulator of G-protein signaling 14  Q-203  0.67055416
Q9BVI0  PHD finger protein 20  Q-203  0.67055416
Q93074  Mediator of RNA polymerase II transcription subunit 12  PF-05190457  0.67054135
P51530  DNA replication ATP-dependent helicase/nuclease DNA2  PF-05190457  0.6705413
Q6NS38  DNA oxidative demethylase ALKBH2  AI-10-49  0.67052937
B4DJY2  Transmembrane protein 233  AI-10-49  0.67052513
Q8N807  Protein disulfide-isomerase-like protein of the testis  PF-05190457  0.67051905
P13929  Beta-enolase  AI-10-49  0.67051786
Q9NRJ7  Protocadherin beta-16  AI-10-49  0.67051774
O95751  Protein LDOC1  MK-5046  0.67051023
Q92947  Glutaryl-CoA dehydrogenase, mitochondrial  fenebrutinib  0.67050344
Q96J94  Piwi-like protein 1  fenebrutinib  0.6704877
O15400  Syntaxin-7  adapalene  0.67046946
O00192  Armadillo repeat protein deleted in velo-cardio-facial syndrome  adapalene  0.67046934
Q17RD7  Synaptotagmin-16  CFI-402257  0.6704517
A0PJZ3  Glucoside xylosyltransferase 2  MK-5046  0.67042667
Q53GG5  PDZ and LIM domain protein 3  PF-05190457  0.6704057
P20929  Nebulin  PF-05190457  0.6704056
Q5NDL2  EGF domain-specific O-linked N-acetylglucosamine transferase  abemaciclib  0.67039376
Q10570  Cleavage and polyadenylation specificity factor subunit 1  fenebrutinib  0.6703786
Q53FE4  Uncharacterized protein C4orf17  AI-10-49  0.67036396
Q96T21  Selenocysteine insertion sequence-binding protein 2  cilofexor  0.67036384
P17980  26S proteasome regulatory subunit 6A  PF-05190457  0.67036086
Q8TE77  Protein phosphatase Slingshot homolog 3  tropifexor  0.67035466
Q96LD4  E3 ubiquitin-protein ligase TRIM47  tropifexor  0.67035466
P25205  DNA replication licensing factor MCM3  fenebrutinib  0.6703515
Q9NQC7  Ubiquitin carboxyl-terminal hydrolase CYLD  fenebrutinib  0.6703515
Q71F23  Centromere protein U  NMS-P715  0.6703202
P46778  60S ribosomal protein L21  fenebrutinib  0.67028475
Q04727  Transducin-like enhancer protein 4  AI-10-49  0.6702773
O14556  Glyceraldehyde-3-phosphate dehydrogenase, testis-specific  AI-10-49  0.6702773
Q92994  Transcription factor IIIB 90 kDa subunit  fenebrutinib  0.67027074
Q15646  2'-5'-oligoadenylate synthase-like protein  fenebrutinib  0.67027074
O15131  Importin subunit alpha-6  fenebrutinib  0.6702412
Q14254  Flotillin-2  fenebrutinib  0.6702412
O75764  Transcription elongation factor A protein 3  CFI-402257  0.67017365
P40425  Pre-B-cell leukemia transcription factor 2  MK-5046  0.67016166
O43766  Lipoyl synthase, mitochondrial  PF-05190457  0.67014426
Q969L2  Protein MAL2  fenebrutinib  0.67013794
Q9NSG2  Uncharacterized protein C1orf112  CCT137690  0.67013377
Q9H892  Tetratricopeptide repeat protein 12  PF-05190457  0.67012644
O95248  Myotubularin-related protein 5  CCT137690  0.6701216
O60481  Zinc finger protein ZIC 3  PF-05190457  0.670091
Q9UBK8  Methionine synthase reductase  AI-10-49  0.6700795
Q4G0J3  La-related protein 7  CCT137690  0.67007875
Q8WW32  High mobility group protein B4  CCT137690  0.67005986
P23297  Protein S100-A1  MK-5046  0.67002577
Q8TCB7  tRNA N  elbasvir  0.6700179
Q8IXH6  Tumor protein p53-inducible nuclear protein 2  abemaciclib  0.67000955
Undruggable human disease-associated proteins selected by ProtalCG
tocsubsectionTable REF : Chemicals interacted with undruggable human proteins
<TABLE>When we consider the proteins in Tbio, there are 9545 proteins which are not int Casas's druggable proteins. If 0.67 was used as the cutoff, 219 proteins were predicted as positive hits. The gene enrichment analysis result for these proteins was listed in Table SREF . Disease associated with these 219 human proteins were also listed in Table SREF . Since one protein is always related with multiple diseases, these diseases are ranked by the number of their associated proteins and the top 10 diseases were listed in the table. Most of top ranked diseases are related with cancer development. 21 drugs that are approved or in clinical trial are predicted to interact with these proteins as shown in Table SREF .
If the proteins in Tbio were removed from the undruggable list, only 2930 proteins were left. If 0.67 was used as the cutoff, there will be only 41 proteins predicted positive and no significant enrichment with David gene enrichment analysis. So 0.665 was used as a cutoff, and 348 proteins were predicted as positive hits. The gene enrichment analysis result for these proteins was listed in Table SREF . Disease associated with these 348 human proteins were also listed in Table SREF . 42 drugs that are approved or in clinical trial are predicted to interact with these proteins as shown in Table SREF .
tocsubsectionTable REF : Functional Annotation enrichment for human proteins in Tbio selected by PortalCG
<TABLE>tocsubsectionTable REF : Top ranked diseases associated with proteins in Tbio selected by portal learning
<TABLE>tocsubsectionTable REF : Chemicals interacted with human proteins in Tbio
<TABLE>tocsubsectionTable REF : Functional Annotation enrichment for undruggable human disease proteins without Tbio selected by PortalCG
<TABLE>tocsubsectionTable REF : Top ranked diseases associated with undruggable human proteins excluding Tbio selected by portal learning
<TABLE>tocsubsectionTable REF : Chemicals interacted with undruggable human proteins excluding Tbio
<TABLE>tocsubsectionTable REF : Model architecture configuration
<TABLE>
Related works 
OOD generalization in deep learning
The recent work Invariant risk minimization (IRM)[10]} is a dedicated algorithm to OOD generalization, which is under the goal of transformative solution for invariant representation. However, given its completeness in theory, many experiments [38]} report IRM are not doing well in large real-world data set.
Many deep learning tasks are inherently OOD generalization. Among those jargon, some are famous for defining a type of OOD scenario problem, for example, Domain generalization [39]} can be taken as the equivalent of OOD generalization; domain shift [39]} rephrases the fact of distribution change in terms of \(D(X,y)\) . Some jargon define a type of solution: domain alignment [41]} minimizes the difference/distance between source domains and target domains distributions for an invariant representation where the distance between source and target domain distributions are measured by a wide variety of statistical distance metrics from simple \(l_2\) , \(f-divergence\)  to Wasserstein distance; domain adaptation [42]} is to leverage pretrained model on a different domain and is just one idea to achieve domain generalization, the more general term that is equivalent to OOD generalization in a more practical sense; causal learning is proved by [8]} to be equivalent to OOD generalization when causality makes senses (taking into consideration the existence of cases where causality is meaningless); robust optimization [44]} that focuses on worst-group performance instead of the average one in ERM; although robust optimization has not quite been adapted to modern deep learning, its sub-field distributional robust optimization [45]} has witnessed quite a few recent works adapted to be used in deep learning.
Worth to be clarified that, many works that are solving the sub-group or sub-population shift problem is quite different from the OOD generalization problem as discussed in the setting of dark chemical genomics space. Sub-population shift is more like a imbalanced data problem where the test set has major resemblance with training data just the shift from a major class to a minor class or vise-versa. For example, GroupDRO [46]} was published in 2018 to address this problem, proposing to incorporate structural assumptions on distribution, which could be straight forward in some data sets which has more meta-data or is a multi-label classification case where the label structure could be used as the structural assumption.

Portal learning key components related
(Model architecture)
Even since the debut of the survey [47]} enlightening the perspective of representation learning, enormous research passion is motivated for model architecture design, almost taken as equivalent to deep learning and overshadowing all other directions. A key idea that echos the demand of generalization is to learn global representation which helps to decrease both \(TrainError(f_{i}^{iid})\)  and known space generalization gap, denoising large data set. Hence, to solve OOD, good model architecture design is not enough.
All existing work in CPI is confined in the known space and limited works have concerned generalization. Generally, proposed CPI deep learning models follow the same fashion: build model architecture of three key modules, protein descriptor, chemical descriptor and interaction learner formulating a classification problem with a few variants as regression problem. Innovation is seen mostly for model architecture, particularly active for chemical descriptor, reflecting all milestones in recent years deep learning advancement from CNN, LSTM to Transformer and GNN as demonstrated in DeepPurpose [48]}. Generalization has not shown in any previous work as a main goal of research except for DISAE[21]} which proves generalizability to orphan GPCR protein drug screening mainly relying on a general purpose pretrained protein language model. It's fine-tuned on GPCR data set with shifted evaluation. Hence, DISAE becomes the baseline model in this work.
(Model intialization)
Although could be categorized as a type of representation learning, transfer learning became an iconic independent concept for its huge success with breakthroughs in many NLP and CV benchmark tasks. It features a pretraining-finetuning procedure. An intuitive example is to pretrain a language model on large general English vocabulary with pretext task formulation such as predicting next word and then to finetune the language model on specific downstreawm task such as machine translation in biology domain. Well-renowned Transformer based pretrained models starting from human language models are a combined success of attention based model architecture design and transfer learning. In the computation biology field, most eye-catching equivalent is protein language model, i.e. protein descripto, which inspired several similar works at the same time by different groups: TAPE and ESM showcases pretraining on large protein vocabulary could significantly improves downstream task such as protein-protein interaction prediction; MSA-based-tranformer and DISAE incorporates MSA in pretraining. From the perspective of the target downstrem task, the power of transfer learning comes from a better model initialization. This is a major breakthrough that could fill the gap of \(TestError(f_{t}^{OOD}) - TestError(f_{t}^{iid})\)  but not necessarily, depending on how it's incorporated into the whole training scheme at system level, particularly depending on data fed in.
DISAE is used in our work here as a pretrained protein descriptor. This choice over other protein language models is due to the fact that DISAE is the smallest among other in terms of memory required to use and optimize with same level of performance. STL is a way to leverage transfer learning to fine better model initialization. The main difference and innovation is that transfer learning naively relies on the belief that more general knowledge transferred will bring better performance while STL in portal learning actively leverage biology endorsed biased when transferring general knowledge. Further, by defining the goal “to learn the portal”, which will be closer to global optimum in target universe loss landscape, the whole training system is steered actively solve ODD.
(STL ) Sparked by the breakthrough of Alphafold 1 [28]} and Alphafold 2[51]} in protein structure prediction, deep learning has been trusted in molecule interaction distance map prediction to learn structure information. The inclusion of CPI-structure, i.e. protein function prediction portal calibration is inspired by recent success in protein structure prediction led by the great work of AlphaFold1[28]} and AlphaFold2[51]}. Specifically, we pretrain the model to predict residue-residue contacts for a protein whose structure is solved and chemical atom-protein residue contacts given a known CPI complex structure. There are three popular ways of residue-residue pairwise distance matrix prediction depending on how to formulate it as a machine learning task. On the one end is to formulate it as a binary classification where a distance threshold is set defining whether a pair of residues are in contact or not, hence the name contact prediction. On the other end is to formulate it as a regression problem where the exact distance is used as a regression target, hence the name exact distance prediction. AlphaFold1 showed another way in between the two ends, which is to formulate it as a multi-class classification problem, where the distribution of pair-wise residue distances is broken down into multiple class labels according to a histogram, hence the name distogram prediction. We first focus on residue-atom pair wise distance at binding sites and then experiments contact prediction and distogram prediction. In our results, the two formulations have similar performance in light of the final CPI prediction through ablation study as shown in Supplemental Figure SREF .
(OOC-ML) It's long be aware that the sequence order of training data exposed to the model has an impact on model generalizability. Active learning [54]} emphasises to actively query data in a iterative fashion to only expose the model to data close to he decision boundary . Curriculum learning [55]} emphasises to sort all training so that the model is exposed to challenges of increasing difficulty. This element of data logistics has also been closely weaved into many optimization algorithms that aim to improve model generalizability. For example, contrastive loss[56]} requires certain ratio of positive v.s. negative samples in each mini-bath. Most related to portal learning is meta-learning which can be categorized into metric-based, model-based and optimizer based “learn to learn” algorithms [57]} with application to few-shot learning and zero-shot learning. Meta-learning started for the data-efficiency challenge instead of generalization or OOD. Although meta-learning is defined very general, making many algorithms seem to be mere an variants falling under its umbrella, in practice, algorithms proposed bearing the name of meta-learning are defined on multi-class classification data set, typically image classification, where the main challenge is the huge number of classes while limited data points are known in each class. Because of this underlying motivation, meta-learning features a very involving data logistics with multiple layer of optimization each has its meta-train/meta-test set sampled based on label distribution. These unspecified facts reveal that there is no existing meta-learning algorithm fit into CPI data.
However, the idea of “learn to learn” is attractive. MAML[32]} is the optimization based meta-learning work that inspired OOC-ML proposed as a major component of portal learning. The differences are major. OOC-ML algorithm expands on it by focusing on data feature distribution instead of label distribution, encouraging active sampling in local neighborhood, which simplifies the support/query meta-train/meta-test data logistics, and ensembling a few local loss directions to learn global gravity direction.

Additional figures
tocsubsectionFigure REF : Dark space statistics histogram
<FIGURE>tocsubsectionFigure REF : Dark space statistics trend line
<FIGURE>tocsubsectionFigure REF : Dark space statistics heatmap
<FIGURE>tocsubsectionFigure REF : Model performance breakdown to each class
<FIGURE>tocsubsectionFigure REF : Model performance t-test
<FIGURE>tocsubsectionFigure REF : Stress model selection performance curves against DISAE as baseline
<FIGURE>tocsubsectionFigure REF : Model performance histogram
<FIGURE>tocsubsectionFigure REF : The binding conformations and 2D-interactions of Fenebrutinib on the targeted proteins predicted by using Autodock
<FIGURE>tocsubsectionFigure REF : The binding conformations and 2D-interactions of Fenebrutinib on the targeted proteins predicted by using Autodock
<FIGURE>tocsubsectionFigure REF : The binding conformations and 2D-interactions of NMS-P715 on the targeted proteins predicted by using Autodock
<FIGURE>tocsubsectionFigure REF :Histogram equalization results
<FIGURE>tocsubsectionFigure REF : Ablation study
<FIGURE>tocsubsectionFigure REF : Model architecture illustration
<FIGURE>